Problem

A fuel cell manufacturer can hire union, non-union permanent, or temporary help. She has a contract to produce at the rate of 2,100 fuel cells per day and would like to achieve this at minimum cost. Union workers work 7 hours per day and can make up to 10 fuel cells per hour. Their wages and benefits cost the company $15.00 and $7.00 per hour, respectively. Union workers are assured that there will be no more than 80% of their number working in non-union permanent positions and that there will be no more than 20% of their number working in temporary positions. Non-union permanent workers work 8 hours per day and can also make up to 10 fuel cells per hour. Their wages are the same as the union employees, but their benefits are worth only $3.00 per hour. Temporary workers work 6 hours per day, can make up to 5 fuel cells per hour, and earn only $10 per hour. They do not receive any benefits.

How many union, non-union, and temporary workers should be hired to minimize the cost to the manufacturer? What is the average cost of producing a fuel cell?